TopCoder SRM 637

Division 1
Problem 250:
SRM 637 Div1 (250) - GreaterGame

Solution:
To find the expectation, first sort the cards on each hand. Then for each of the known Sothe's card, we can determine whether we want to top the card with the lowest possible card on our hand, or just lose with the lowest possible card. Each of the card that we topped will contribute to the expectation by 1, and those we lose contribute 0. Then we will end up with the cards that Sothe did not reveal, and the cards that we do not used yet. For each card on our hand, we find the probability of our card winning given the knowledge of Sothe's remaining cards. Each of the probability contributes to our expectation. Hence we just sum up all the probabilities with the number of the cards that we won earlier on.